Ample vector bundles and polarized manifolds of sectional genus three

Let E be an ample vector bundle of rank r \geq 2 on a smooth complex projective variety of dimension n having a global section whose zero locus Z is a smooth subvariety of dimension n-r \geq 3 of X. Let H be an ample line bundle on X such that its restriction H_Z to Z is generated by global sections. The structure of triplets (X,E,H) is determined under the assumption that (Z,H_Z) has sectional genus g(Z,H_Z)=3.